Question

When 2x^3-x^2-13x+k is divided by x-2 the remainder is-20.Find the value of k​

Answer 1

Answer:

Let

$f(x) = 2 {x}^{3} - {x}^{2} - 13x + k$

Remainder when dividing by x-2 = 0 or x=2

will be equal to f(2) .

$f(2) = - 20 \\ \\ 2( {2}^{3} ) - {2}^{2} - 13(2) + k = - 20 \\ \\ 16 - 4 - 26 + k = - 20 \\ - 14 + k = - 20 \\ k = - 6$